That is according to North Yorkshire County Council which first secured funding five years ago and has recently faced design and safety complaints over the first phase of works completed in January.
The council - which is now reviewing designs for the final two phases - said the cycle path has so far been delivered to the expected costs and that it currently did not anticipate "any overspend".
The project is part of a wider package of transport improvements for the west of Harrogate which once completed will cost around £4.6 million.
Around £2 million of this was allocated for the Otley Road cycle path, and so far £1.6 million has been spent on design, construction and utility costs, according to the council.
This is made up of £1.04 million on phase one and £559,182 on phase two which has yet to begin.
A council spokesperson said: "Invoices are still due for phase one, and phase two has yet to be started therefore costs will increase, however we are on budget."
Red Arrows set to fly over Harrogate district on Thursday afternoon
Phase one and two are being funded by the government's National Productivity Investment Fund, while phase three will be built using contributions from housing developers planning to build hundreds of new homes in the west of Harrogate.
Kevin Douglas, chairman of Harrogate District Cycle Action, said the campaign group had been given "no indication" of how these negotiations with developers were progressing and that this was a "worry" for when the project could be completed in full.
He added: "The main issue for us is the time this project has taken already and with the further delays surely that means the costs are going to go up.
"Hopefully the council keeps within budget for the whole project and it gets delivered in full soon."
His comments come after members of Harrogate District Cycle Action recently met with council officials to highlight their concerns over the first phase.
Parts of the completed works have been described as "unsafe" and “badly designed," with a narrowed section of cycle path at Otley Road’s junction with Harlow Moor Road being a particular concern.
The council is currently in talks with Yorkshire Water to buy a small plot of land in order to remove a wall and widen a corner on this part of the route.
The council also said it would take all feedback onboard as part of its review of phases two and three which are being redrawn in line with new government guidance.
Mr Douglas added: "The higher quality cycle path we get, the more people will use it - that has always been our view as we want a scheme that delivers facilities which everyone can use.
"We also want lessons to be learnt from the first phase, and hopefully there is a genuine willingness to take on board the points we made."
The council previously said it hoped to start work on phase two in April.
However, this is now likely to be in May or June.
By Jacob Webster, Local Democracy Reporter